ABSTRACT Our research is focused on fundamental questions related to cell polarity. Cell polarity describes the ability of cells to spatially organize their internal constituents along a specific axis. It is critical for cell migration (where cells need to generate a front and a back), and also for developing specialized cell shapes that are needed for many cells to function. In addition, derangements of the polarity machinery can contribute to several diseases, for example by enabling cancer metastases. Thus, an understanding of the mechanisms, regulation, and consequences of cell polarity is of both fundamental and medical interest. Studies on cell polarity have identified an evolutionarily ancient and conserved core machinery centered on a ?master regulator? of polarity called Cdc42. However, many of the most interesting questions remain unsolved. How is it that most cells only make a single ?front? enriched in Cdc42, but some cells with more complex shapes can specify several sites to act as fronts? How do cells read their environment to determine the direction in which they should orient the polarity axis? Once polarity is established, how is the precise downstream set of events orchestrated to give each cell type the right shape? And then, how do cells know what shape they are? We use the uniquely tractable yeast model system to investigate these questions, and apply a combination of cutting-edge microscopy, genetics, and computational modeling. Our previous work identified a positive feedback mechanism that explains how Cdc42 becomes concentrated at polarity sites to establish a polarity axis. Our recent work on polarization during yeast mating, when yeast cells orient in response to spatial gradients of pheromones, suggests a new paradigm for tracking chemical gradients. And our work on a yeast cell-cycle checkpoint responsive to cell shape now suggests a model for how cells know what shape they are. Based on these findings, we are poised to make significant advances on the questions posed above, and to exploit the answers to those questions to provide insights that extend well beyond the yeast system.